Terms Of Multiple Reflections Research Articles

Sound diffusers based on sonic crystals.

A sound diffuser is proposed based on sonic crystals, structures formed by a periodic distribution of cylindrical scatterers in a host medium, which is usually air. The diffuser is a so-called biperiodic structure, as formed by two arrays of sonic crystals with slightly different periodicities. Large diffusivity at low frequencies is achieved when the typical scale of the blocks is much larger than the periodicity of the crystals, determined by its lattice constant. An interpretation of the low frequency behavior of the diffuser is given in the homogenization limit in terms of multiple reflections and interference between the fields scattered by the different blocks. It is also shown that sonic crystal based diffusers enhance time spreading in comparison with other conventional diffusers.

Edge effects in graphene nanostructures: From multiple reflection expansion to density of states

We study the influence of different edge types on the electronic density of states of graphene nanostructures. To this end we develop an exact expansion for the single particle Green's function of ballistic graphene structures in terms of multiple reflections from the system boundary, that allows for a natural treatment of edge effects. We first apply this formalism to calculate the average density of states of graphene billiards. While the leading term in the corresponding Weyl expansion is proportional to the billiard area, we find that the contribution that usually scales with the total length of the system boundary differs significantly from what one finds in semiconductor-based, Schr\"odinger type billiards: The latter term vanishes for armchair and infinite mass edges and is proportional to the zigzag edge length, highlighting the prominent role of zigzag edges in graphene. We then compute analytical expressions for the density of states oscillations and energy levels within a trajectory based semiclassical approach. We derive a Dirac version of Gutzwiller's trace formula for classically chaotic graphene billiards and further obtain semiclassical trace formulae for the density of states oscillations in regular graphene cavities. We find that edge dependent interference of pseudospins in graphene crucially affects the quantum spectrum.

Multipathing and spectral modulation of the downgoing wavefield in a complex crust: an example from the KTB (Germany) borehole

VSP data collected in the KTB (Germany) borehole to a depth of 8.5 km in 1999 show a surprising spectral modulation of the downgoing wavefield. After filtering the data with the singular value decomposition technique it was found that below about 6.2 km there are two depth intervals where the modulation can be explained in terms of a basic wavelet plus two weighted and delayed copies of that wavelet, with the delay for each wavelet remaining almost constant in each interval. The boundary between the two intervals is at about 7.25 km depth and above and below this depth the delay for the second wavelet is almost the same, while the delay for the third wavelet is significantly different. Neither the modulation nor its depth variation are source related and cannot be explained in terms of multiple reflections in a subhorizontal low-velocity layer. On the other hand, finite difference synthetic data show that subvertical layering (which is prevalent in the borehole area) provides a mechanism that can explain the observations. This mechanism has analogies with the generation of the standard refracted (i.e. head) waves. When a plane wave front propagates perpendicular to the boundaries of a vertical low-velocity layer surrounded by two vertical high-velocity layers, refracted wave fronts are generated in the low-velocity layer, which in turn generate secondary wave fronts in the high-velocity layers. These wave fronts trail the primary wave fronts by a constant delay whose magnitude has a simple dependence on the thickness of the low-velocity layer and the velocities involved. This process creates multipath arrivals that in geological settings with steeply inclined and faulted layers may appear and disappear rather abruptly, which may contribute to a scattered appearance of the wavefield.

Surface reflectance model of forests with a consideration of interactions among trees in terms of multiple reflections by means of Monte-Carlo simulations together with experiments

Surface reflectance model of forests with a consideration of interactions among trees and land surface including grasses in terms of multiple reflections by means of Monte-Carlo simulations together with experiments is proposed. The Monte Carlo method statistically simulates the paths of photons inside the atmosphere and the forested area to clarify the behaviors of individual photon. The radiance on ellipse and cone types of canopy calculated agreed well with the measured. Influences due to shape of the trees, trunk tree distance, and ratio of horizontal and vertical size of the trees and so on to the parameter estimation are clarified with the experimental results. It is found that a few to more than 10% of influence due to multiple reflections among trees are anticipated. The potentialities of the code are then depicted over different types of forests including coniferous and broadleaf canopies.

Acoustics of an obstacle inside a reactive silencer

The transmission and reflection of sound in a cylindrical duct containing several discontinuities is investigated. A building-block method, which gives the transmission and reflection matrices for a complex system from those of the parts, is applied to bifurcations, sudden area changes with or without extended inlets, and spherical obstacles (which may be lossy). In some cases the solution can be interpreted in terms of multiple reflections. When the lengths between the discontinuities are small it is important to include also non-propagating modes, and this is especially true when the sudden area change is obtained from the area change with extended inlet in the limit of vanishing inlet. For an expansion chamber (a portion of the duct with larger radius) with or without an obstacle and with or without inlets a number of numerical results with variation in frequency are presented. Numerical results for the various building-block elements of the expansion chamber are also considered.

The reflectance of dendritic-tungsten surfaces

The relatively low total optical reflectance measured from the surface of dendritic tungsten is quantitatively explained in terms of multiple reflections from the surface structure. A geometrical optical model is found to adequately describe the multiple reflections from dendrites which have an average spacing of about 5 μm. Coefficients representing the fraction of light reflected a given number of times are determined by analysis of the total reflectance of the dendritic surface on which an antireflective coating has been formed by anodization. At most wavelengths, second-order reflection (or light twice reflected) is found to dominate the reflectance of the dendritic surface for angles of incident light up to about 60° from normal, beyond which the first-order reflection becomes dominant. Based on the model, the reflectance of a geometrically characterized dendritic surface can be predicted for any type and thickness of antireflective coating.

Asymptotic overtone structure in eigenfrequencies of torsional normal modes of the Earth: a model study

Summary. The study of the asymptotic behaviour of eigenfrequencies of torsional modes of the Earth is of interest in the problem of the existence of discontinuities in the Earth's interior and the determination of their depth and scale, since the solotone effect, which is a persistent oscillatory cohponent in the asymptotic overtone structure, is very sensitive to the presence of discontinuities. The asymptotic behaviour of torsional eigenfrequencies of the second order differential equation for the Earth's free oscillations can be compared with that obtained from eigenfrequencies evaluated from synthetic SH-wave seismograms by Brune's phase correlation method, using various earth models. The solotone effect that appears in the former for discontinuous models can be explained in terms of multiple reflections fram the discontinuities, and can be reconstructed from synthetic SH-wave pulses arising from these reflections. Its properties vary systematically with the depth and the scale of discontinuities and can be superposed for several discontinuities.

Rays, Beams, and Modes Pertaining to the Excitation of Dielectric Waveguides

The two-dimensional problem of excitation of an inhomogeneous dielectric layer by a Gaussian beam is considered, with emphasis on useful representations that treat the field either in terms of multiple reflections or in terms of guided modes. A recently developed method is employed whereby the beam fields are generated from line source fields by assigning a complex value to the source coordinates. When applied to the asymptotic solution for the line source field, this procedure furnishes a simple and quantitative relation between line-source-excited ray optics and paraxial beam optics. It also clarifies the role of lateral ray and beam shifts for reflection at a boundary with incidence-angle-dependent reflection coefficient, especially when multiply reflected fields are converted into modal form. Results are given for beams which are reflected at both boundaries, reflected at one boundary and refracted before reaching the other boundary, and trapped by refraction without reaching either boundary. In the first case, conversion to modal form is more convenient at large distances whereas in the latter case, paraxial beam tracking is preferable.

High-Frequency Scattering by a Transparent Sphere. II. Theory of the Rainbow and the Glory

The treatment, initiated in Paper I [J. Math. Phys. 10, 82 (1969)], of the high-frequency scattering of a scalar plane wave by a transparent sphere is continued. The main results here are an improved theory of the rainbow and a theory of the glory. The modified Watson transformation is applied to the third term of the Debye expansion of the scattering amplitude in terms of multiple reflections. Only the range 1<N<√2, where N is the refractive index, is considered. In the geometrical-optic approximation, this term is associated with rays transmitted after one internal reflection, and there are three angular regions, corresponding to one ray, two rays, or no ray (shadow) passing through each direction. Together with transition regions, this leads to six different angular domains. In the 1-ray and 2-ray regions, geometrical-optic terms are dominant. Correction terms corresponding to the 2nd-order WKB approximation are also evaluated. In the 0-ray region, the amplitude is dominated by complex rays and surface waves. The 1-ray/2-ray transition is a Fock-type region. The rainbow appears in the 2-ray/0-ray transition region. The extension of the method of steepest descents due to Chester, Friedman and Ursell is applied. The result is a uniform asymptotic expansion for the scattering amplitude. It reduces to Airy's theory in the lowest-order approximation, but its domain of validity is considerably greater, both with regard to size parameter and to angles. The glory is an example of strong ``Regge-pole dominance'' of the near-backward scattering amplitude. Van de Hulst's conjecture that surface waves are responsible for the glory is confirmed. However, besides surface waves taking two shortcuts through the sphere, higher-order terms in the Debye expansion must also be taken into account. By considering also the effect of higher-order surface-wave contributions, all the features observed in the glory (apart from the polarization) are explained. Resonance effects associated with nearly-closed paths of diffracted rays lead to large, rapid, quasiperiodic intensity fluctuations. The same effects are responsible for the ripple in the total cross-section. Similar fluctuations appear in any direction, but their amplitude increases with the scattering angle, becoming a maximum near the backward direction, where they are dominant. They can also be interpreted as a collective effect due to many nearly-resonant partial waves in the edge domain. The dominant surface-wave contributions can also be summed to all orders for N < 1, leading to a renormalization of the propagation constants of surface waves.

Conjugate echoes in Alouette-2 topside-sounder data

Three types of ionograms containing symmetric conjugate echo traces which appear frequently in the Alouette-2 satellite topside-sounder data are presented and explained in terms of multiple reflections between conjugate points of the field line passing through the satellite. Such symmetric traces have not been previously reported in the literature. The high intensity of these traces gives credence to the existence of magnetospheric waveguides along which signals can propagate with very little attenuation.

Polarisation of atmospheric pulses due to successive reflections at the ionosphere

Measurements of the polarisation of successive pulses in echo-type atmospherics have been made at frequencies of 8 kc/s and 12 kc/s. The results have shown that the first few sky waves are nearly plane polarised, but that as the order of reflection increases the polarisation becomes more and more elliptical. The theoretical problem of the propagation of v.l.f. radio waves between the Earth and the ionosphere has been examined with particular reference to the calculation of theoretical values of polarisation. By a comparison of the theoretical values with those obtained experimentally, the appropriate reflection coefficients are derived for the Earth-ionosphere propagation system. It is suggested that the polarisation pattern of night-time echo trains can be explained in terms of multiple reflections between the ground and an ionospheric layer having a high electron density gradient in the lower fringes of the E-region.